Mixed motives and algebraic K-theory. (Almost unchanged version of the author's habilitation at Univ. Regensburg 1988)

Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Generalizations (algebraic spaces, stacks) (14A20) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (86)

Torsion properties of modified diagonal classes on triple products of modular curves ⋮ Motives over totally real fields and $p$-adic $L$-functions ⋮ Hodge realization of Voevodsky motives ⋮ Higher order operations in Deligne cohomology ⋮ Higher $l$-adic Abel-Jacobi mappings and filtrations on Chow groups ⋮ Regulators for Rankin-Selberg products of modular forms ⋮ On the $p$-adic height of Heegner cycles ⋮ Hirzebruch-Zagier cycles and twisted triple product Selmer groups ⋮ On an elliptic analogue of Zagier's conjecture ⋮ Motivation for Hodge cycles ⋮ THE RIGID SYNTOMIC RING SPECTRUM ⋮ On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field ⋮ Height functions for motives ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ Recent progress on the Tate conjecture ⋮ Selmer groups and central values of $L$-functions for modular forms ⋮ Nonvanishing of Hecke $L$-functions and the Bloch-Kato conjecture ⋮ Families of motives and the Mumford-Tate conjecture ⋮ On the elliptic Stark conjecture in higher weight ⋮ Surjectivity of cycle maps for singular varieties ⋮ Sects ⋮ The fundamental group of an extension in a Tannakian category and the unipotent radical of the Mumford-Tate group of an open curve ⋮ On unipotent radicals of motivic Galois groups ⋮ A pro-algebraic fundamental group for topological spaces ⋮ On the Tate conjecture for divisors ⋮ Recent trends in algebraic geometry. Abstracts from the workshop held June 18--23, 2023 ⋮ Etale homotopy and sums-of-squares formulas ⋮ On the Northcott property for special values of $L$-functions ⋮ Algebraic rational cells and equivariant intersection theory ⋮ Deligne periods of mixed motives, $K$-theory and the entropy of certain $\mathbb {Z}^n$-actions ⋮ On local monodromy filtrations attached to motives ⋮ The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties. ⋮ Generalized Poincaré Classes and Cubic Equivalences ⋮ Arithmetic diagonal cycles on unitary Shimura varieties ⋮ On the structure of Selmer and Shafarevich–Tate groups of even weight modular forms ⋮ $\mathbb Q$-motives and modular forms ⋮ Generalized Heegner cycles on Mumford curves ⋮ Kähler–de Rham Cohomology and Chern Classes ⋮ Unnamed Item ⋮ On the Abel-Jacobi maps of Fermat Jacobians ⋮ Higher regulators, Hilbert modular surfaces, and special values of $L$-functions ⋮ The Abel-Jacobi map for higher Chow groups. II ⋮ A Lefschetz (1,1) theorem for normal projective complex varieties ⋮ Indecomposable cycles and arithmetic normal functions ⋮ The Arason invariant and mod 2 algebraic cycles ⋮ The Tamagawa number conjecture of adjoint motives of modular forms ⋮ Groupes fondamentaux motiviques de Tate mixte ⋮ Cohomological Hasse principle and motivic cohomology for arithmetic schemes ⋮ Correspondences and singular varieties ⋮ Emergent spacetime from modular motives ⋮ Motivic torsors ⋮ Big Heegner points and generalized Heegner cycles ⋮ Filtrations on Chow groups and transcendence degree ⋮ Techniques, computations, and conjectures for semi-topological $K$-theory ⋮ Weights in arithmetic geometry ⋮ Arithmetic cohomology over finite fields and special values of $\zeta$-functions ⋮ The Leray spectral sequence is motivic ⋮ Recent developments on noncommutative motives ⋮ Generalised Heegner cycles and the complex Abel-Jacobi map ⋮ Lectures on Hodge theory and algebraic cycles ⋮ Hasse principles for higher-dimensional fields ⋮ Quadratic Chabauty for modular curves and modular forms of rank one ⋮ Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations. II: Wild case ⋮ On log motives ⋮ Étale motives ⋮ The Néron-Severi group of a proper seminormal complex variety ⋮ A short note on the weak Lefschetz property for Chow groups ⋮ A finiteness theorem for the symmetric square of an elliptic curve ⋮ Higher Chow groups and the Hodge-${\mathcal D}$-conjecture ⋮ Heights and Tamagawa numbers of motives ⋮ Equivariant motives ⋮ One-motives and a conjecture of Deligne ⋮ Syntomic cohomology and Beilinson’s Tate conjecture for 𝐾₂ ⋮ Abel-Jacobi mappings and finiteness of motivic cohomology groups ⋮ Torsion zero-cycles on the self-product of a modular elliptic curve ⋮ Arithmetic normal functions and filtrations on Chow groups ⋮ Algebraic independence in the Grothendieck ring of varieties ⋮ Un crit\`ere d'\'epointage des sections $l$-adiques ⋮ Hodge cycles and the Leray filtration ⋮ On a conjectural filtration on the Chow groups of an algebraic variety. I: The general conjectures and some examples ⋮ A weak Lefschetz result for Chow groups of complete intersections ⋮ Kolyvagin's method for Chow groups and Kuga-Sato varieties ⋮ $K$-theory of curves over number fields ⋮ On Chow-weight homology of geometric motives ⋮ On the image of the 𝑙-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field ⋮ CHOW GROUPS, CHOW COHOMOLOGY, AND LINEAR VARIETIES

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